Question

A gas in a piston cylinder assembly undergoes an expansion process where $P{V}^{1.5}=$ constant. The initial pressure is $3bar$, the initial volume is $0.1m^3$ and the final volume is $0.2m^3$. Determine the work done for this process.

• A. $+17.6kJ$
• B. $-17.6kJ$
• C. $+13.2kJ$
• D. $-13.2kJ$

Answer 1

The correct option is A $+17.6kJ$

Given $P{V}^{1.5}=$constant
$\Rightarrow P_1{V}_1^{1.5}=P_2{V}_2^{1.5}$

$P_2=P_1{\left(\frac{V_1}{V_2}\right)}^{1.5}=3\times {10}^5{\left(\frac{0.1}{0.2}\right)}^{1.5}=1.06\times {10}^{5}Pa$

Work done is given by
$W=\frac{P_2{V}_2-P_1{V}_1}{1-n}=\frac{(1.06\times {10}^5)\left(0.2\right)-(3\times {10}^5)\left(0.1\right)}{1-1.5}=17.6kJ$
Option A.